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mikedagr8
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Set notation help and other things
« on: Apr 20th, 2008, 5:17am » |
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G'day guys, I'm doing my holiday homework and I don't understand this question as well as a few others. Could you please help me out?
The question states:
For A = {3,4,7,8} and B = {2,3,4,6,10} describe:
B/A
Does this just mean I divide the elements? What does this actually mean, and how do I do it.
Thanks again.
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ThudnBlunder
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Re: Set notation help and other things
« Reply #1 on: Apr 20th, 2008, 5:40am » |
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I believe it means the set of members of A that are not in B.
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mikedagr8
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Re: Set notation help and other things
« Reply #2 on: Apr 20th, 2008, 5:42am » |
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Ah, that would make sense. Thanks TB.
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Obob
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Re: Set notation help and other things
« Reply #3 on: Apr 20th, 2008, 6:11am » |
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That is really bad notation, though! One would typically denote by A\B the set of elements of A that are not in B. The notation B/A often has an entirely different meaning: it is the set B, with some of its elements identified according to the set A. In this particular case, it would be B/A = {2,6,10,{3,4}}. This notion makes more sense when A is contained in B though.
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mikedagr8
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Re: Set notation help and other things
« Reply #4 on: Apr 20th, 2008, 6:17am » |
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Do I write B\A not as {2,6,10} or as {2,6,10{3,4}}?
So, if another question has A = {5,6,7,8,9} and B={2,5,6,9,138}
How would I write A\B
{7,8{5,6,9}} or {7,8}.
Thanks again for the help.
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| « Last Edit: Apr 20th, 2008, 4:55pm by mikedagr8 » |
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ThudnBlunder
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Re: Set notation help and other things
« Reply #5 on: Apr 20th, 2008, 8:33am » |
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Oh, it was B/A, not A/B. 
In which case, I would say B/A denotes the set of members of B that are not in A.
But looking it up, I see that the back slash (\) is used.
Mike, are you sure about the forward slash (/)?
Are there other examples using a back slash?
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Obob
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Re: Set notation help and other things
« Reply #6 on: Apr 20th, 2008, 9:41am » |
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If this is a homework assignment based off a textbook, the only sure fire thing is to look up what notation the textbook uses. If it was given by a teacher, ask the teacher what the notation means. I would be surprised if what they mean by B/A is what I said in the last post. Also make sure that it is in fact a forward slash / and not a backslash \.
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mikedagr8
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Re: Set notation help and other things
« Reply #7 on: Apr 20th, 2008, 4:54pm » |
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on Apr 20th, 2008, 8:33am, ThudanBlunder wrote:Mike, are you sure about the forward slash (/)?
Are there other examples using a back slash?
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Yes (to both quesations), it should be a back slash. At 11:30pm I forget what I am doing. It is corrected now.
Obob, I can't ask them right now, as they are on holidays for another 8 days.
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| « Last Edit: Apr 20th, 2008, 4:57pm by mikedagr8 » |
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Obob
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Re: Set notation help and other things
« Reply #8 on: Apr 20th, 2008, 5:03pm » |
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The notation A\B definitely means the elements of A that are not in B. So in the original example, the answer is {7,8}.
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mikedagr8
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Re: Set notation help and other things
« Reply #9 on: Apr 21st, 2008, 4:20am » |
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on Apr 20th, 2008, 5:03pm, Obob wrote:| The notation A\B definitely means the elements of A that are not in B. So in the original example, the answer is {7,8}. |
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Thanks Obob.
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mikedagr8
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Re: Set notation help and other things
« Reply #10 on: Apr 21st, 2008, 6:19am » |
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Here is some more complex kind of stuff. Yes the pun is intended.
For z=12+16 w=5+12find:
|z|
and
|z+w|
When I type |z| on the calculator I get an answer of 20 and |z+w| 32.75667871..... How does this occur and why? Once again we have not been taught absolute functions of imaginary numbers.
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gotit
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Re: Set notation help and other things
« Reply #11 on: Apr 21st, 2008, 7:09am » |
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If z=a+bi, then |z|=sqrt(a2+b2)
If z=a+bi and w=c+di, then z+w=(a+c)+(b+d)i.
Hope that helps.
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Obob
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Re: Set notation help and other things
« Reply #12 on: Apr 21st, 2008, 9:54am » |
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If you plot the complex number z in the complex plane, then |z| is the length of the line segment joining 0 to z. So |z| really does generalize the notion of absolute value of a real number, since the length of the line segment from 0 to a real number a is just |a|.
An are there really no sections of the textbook to go with these problems? If not, it sounds like a terrible teacher, assigning problems with untaught notation over holiday...
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| « Last Edit: Apr 21st, 2008, 9:55am by Obob » |
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mikedagr8
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Re: Set notation help and other things
« Reply #13 on: Apr 21st, 2008, 6:04pm » |
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on Apr 21st, 2008, 9:54am, Obob wrote:| are there really no sections of the textbook to go with these problems? If not, it sounds like a terrible teacher, assigning problems with untaught notation over holiday... |
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No, he is a wonderful teacher. He just has the highest expectations of our work, and quite often as a class he is disappointed. He wants us to work some things out by ourselves. The chapter in the text book for this does not cover modulus functions of imginary values sufficiently. It does so once when explaining how to multiply and divide 'cis' values, but that is it.
Sorry about that.
Thanks again.
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mikedagr8
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Re: Set notation help and other things
« Reply #14 on: Apr 21st, 2008, 6:36pm » |
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How do I change these equations to polar form. We have done this, but nothing as difficult as this. I have attempted these questions, but could not find an appropriate answer (I feel). Thanks again for the help guys.
For y2=(x3)/(a-x)
I ended up with the equation r=(asin2 )/(cos3+sin2cos) Is this correct and if not what is the correct answer?
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| « Last Edit: Apr 21st, 2008, 6:37pm by mikedagr8 » |
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ThudnBlunder
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Re: Set notation help and other things
« Reply #15 on: Apr 21st, 2008, 11:25pm » |
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Hint: (y/x)2 = x/(a-x)
Substitute for y/x, rearrange, and eliminate x.
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| « Last Edit: Apr 21st, 2008, 11:42pm by ThudnBlunder » |
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mikedagr8
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Re: Set notation help and other things
« Reply #16 on: Apr 21st, 2008, 11:46pm » |
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on Apr 21st, 2008, 11:25pm, ThudanBlunder wrote:Hint: (y/x)2 = x/(a-x)
Substitute for y/x, rearrange, and eliminate x. |
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I'm sorry, but I don't understand.  What do you mean substitue for y/w?
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ThudnBlunder
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Re: Set notation help and other things
« Reply #17 on: Apr 21st, 2008, 11:52pm » |
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on Apr 21st, 2008, 11:46pm, mikedagr8 wrote:
I'm sorry, but I don't understand. What do you mean substitue for y/w? |
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y = rsin(theta)
x = rcos(theta)
So (y/x) = tan(theta)
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mikedagr8
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Re: Set notation help and other things
« Reply #18 on: Apr 21st, 2008, 11:54pm » |
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on Apr 21st, 2008, 11:52pm, ThudanBlunder wrote:
I forgot that. Thanks.
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mikedagr8
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Re: Set notation help and other things
« Reply #19 on: Apr 22nd, 2008, 12:00am » |
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I now arrive at
r = (atan2)/(cos+tan2cos)
Still doesn't look correct though. 
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ThudnBlunder
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Re: Set notation help and other things
« Reply #20 on: Apr 22nd, 2008, 3:41pm » |
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on Apr 22nd, 2008, 12:00am, mikedagr8 wrote:I now arrive at
r = (atan2)/(cos+tan2cos)
Still doesn't look correct though. |
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What does 1 + tan2(theta) equal?
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mikedagr8
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Re: Set notation help and other things
« Reply #21 on: Apr 22nd, 2008, 7:51pm » |
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on Apr 22nd, 2008, 3:41pm, ThudanBlunder wrote:
What does 1 + tan2(theta) equal?
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The only reason I know this is because I'm looking this up in the book. I have not learnt this yet but it is equal to sec2. How does this help?
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| « Last Edit: Apr 22nd, 2008, 7:51pm by mikedagr8 » |
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ThudnBlunder
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Re: Set notation help and other things
« Reply #22 on: Apr 22nd, 2008, 7:55pm » |
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on Apr 22nd, 2008, 7:51pm, mikedagr8 wrote:
It helps if you consider your denominator.
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mikedagr8
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Re: Set notation help and other things
« Reply #23 on: Apr 22nd, 2008, 8:24pm » |
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OK. Does atan2+a/(cos) look better?
Have I made any other errors?
Ah, could it be atan2/(cossec2)?
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| « Last Edit: Apr 22nd, 2008, 8:27pm by mikedagr8 » |
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ThudnBlunder
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Re: Set notation help and other things
« Reply #24 on: Apr 22nd, 2008, 8:32pm » |
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on Apr 22nd, 2008, 8:24pm, mikedagr8 wrote:| OK. Does atan2+a/(cos) look better? |
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No, a(sec - cos) looks better.
But it seems you don't really know what sec means.
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